std::frexp

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frexp
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Defined in header <cmath>
float       frexp( float arg, int* exp );
 (1)
double      frexp( double arg, int* exp );
 (2)
long double frexp( long double arg, int* exp );
 (3)
double      frexp( Integral arg, int* exp );
 (4) (since C++11)
1-3) Decomposes given floating point value arg into a normalized fraction and an integral power of two.
4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (2) (the argument is cast to double).

Parameters

arg - floating point value
exp - pointer to integer value to store the exponent to

Return value

If arg is zero, returns zero and stores zero in *exp.

Otherwise (if arg is not zero), if no errors occur, returns the value x in the range (-1;-0.5], [0.5; 1) and stores an integer value in *exp such that x×2(*exp)
=arg

If the value to be stored in *exp is outside the range of int, the behavior is unspecified.

If arg is not a floating-point number, the behavior is unspecified.

Error handling

This function is not subject to any errors specified in math_errhandling

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

  • If arg is ±0, it is returned, unmodified, and 0 is stored in *exp.
  • If arg is ±∞, it is returned, and an unspecified value is stored in *exp.
  • If arg is NaN, NaN is returned, and an unspecified value is stored in *exp.
  • No floating-point exceptions are raised.
  • If FLT_RADIX is 2 (or a power of 2), the returned value is exact, the current rounding mode is ignored

Notes

On a binary system (where FLT_RADIX is 2), frexp may be implemented as 

{
    *exp = (value == 0) ? 0 : (int)(1 + std::logb(value));
    return std::scalbn(value, -(*exp));
}

The function std::frexp, together with its dual, std::ldexp, can be used to manipulate the representation of a floating-point number without direct bit manipulations.

Example

Compares different floating-point decomposition functions

Run this code
#include <iostream>
#include <cmath>
#include <limits>
 
int main()
{
    double f = 123.45;
    std::cout << "Given the number " << f << " or " << std::hexfloat
              << f << std::defaultfloat << " in hex,\n";
 
    double f3;
    double f2 = std::modf(f, &f3);
    std::cout << "modf() makes " << f3 << " + " << f2 << '\n';
 
    int i;
    f2 = std::frexp(f, &i);
    std::cout << "frexp() makes " << f2 << " * 2^" << i << '\n';
 
    i = std::ilogb(f);
    std::cout << "logb()/ilogb() make " << f/std::scalbn(1.0, i) << " * "
              << std::numeric_limits<double>::radix
              << "^" << std::ilogb(f) << '\n';
}

Possible output: 

Given the number 123.45 or 0x1.edccccccccccdp+6 in hex,
modf() makes 123 + 0.45
frexp() makes 0.964453 * 2^7
logb()/ilogb() make 1.92891 * 2^6


See also

 multiplies a number by 2 raised to a power
(function)
(C++11)
 extracts exponent of the number
(function)
(C++11)
 extracts exponent of the number
(function)
decomposes a number into integer and fractional parts
(function)
C documentation for frexp
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